Invariants
Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $2^{8}\cdot6^{8}\cdot8^{4}\cdot24^{4}$ | Cusp orbits | $2^{4}\cdot4^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24Z5 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}7&12\\47&121\end{bmatrix}$, $\begin{bmatrix}37&180\\158&133\end{bmatrix}$, $\begin{bmatrix}109&0\\133&35\end{bmatrix}$, $\begin{bmatrix}115&144\\252&143\end{bmatrix}$, $\begin{bmatrix}199&108\\233&37\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.192.5.so.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $24$ |
Cyclic 264-torsion field degree: | $960$ |
Full 264-torsion field degree: | $2534400$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
12.192.1-12.e.1.2 | $12$ | $2$ | $2$ | $1$ | $0$ |
264.192.1-12.e.1.4 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.sm.1.14 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.sm.1.23 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.sm.2.14 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.sm.2.23 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.3-264.hh.1.5 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.hh.1.40 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.ih.2.15 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.ih.2.22 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.pv.1.14 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.pv.1.27 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.pv.2.14 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.pv.2.23 | $264$ | $2$ | $2$ | $3$ | $?$ |